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Simplifying 0 = -10a2 + 475a + -3750 Reorder the terms: 0 = -3750 + 475a + -10a2 Solving 0 = -3750 + 475a + -10a2 Solving for variable 'a'. Combine like terms: 0 + 3750 = 3750 3750 + -475a + 10a2 = -3750 + 475a + -10a2 + 3750 + -475a + 10a2 Reorder the terms: 3750 + -475a + 10a2 = -3750 + 3750 + 475a + -475a + -10a2 + 10a2 Combine like terms: -3750 + 3750 = 0 3750 + -475a + 10a2 = 0 + 475a + -475a + -10a2 + 10a2 3750 + -475a + 10a2 = 475a + -475a + -10a2 + 10a2 Combine like terms: 475a + -475a = 0 3750 + -475a + 10a2 = 0 + -10a2 + 10a2 3750 + -475a + 10a2 = -10a2 + 10a2 Combine like terms: -10a2 + 10a2 = 0 3750 + -475a + 10a2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(750 + -95a + 2a2) = 0 Factor a trinomial. 5((10 + -1a)(75 + -2a)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + -1a)' equal to zero and attempt to solve: Simplifying 10 + -1a = 0 Solving 10 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1a = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1a = 0 + -10 -1a = 0 + -10 Combine like terms: 0 + -10 = -10 -1a = -10 Divide each side by '-1'. a = 10 Simplifying a = 10Subproblem 2
Set the factor '(75 + -2a)' equal to zero and attempt to solve: Simplifying 75 + -2a = 0 Solving 75 + -2a = 0 Move all terms containing a to the left, all other terms to the right. Add '-75' to each side of the equation. 75 + -75 + -2a = 0 + -75 Combine like terms: 75 + -75 = 0 0 + -2a = 0 + -75 -2a = 0 + -75 Combine like terms: 0 + -75 = -75 -2a = -75 Divide each side by '-2'. a = 37.5 Simplifying a = 37.5Solution
a = {10, 37.5}
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